SOLUTION: For Biological Science and Education faculties combined, 1/6 of the female and 1/4 of the male faculty members are associate professors. If a person is randomly chosen from these t

Question 1199934: For Biological Science and Education faculties combined, 1/6 of the female and 1/4 of the male faculty members are associate professors. If a person is randomly chosen from these two departments, what is the probability that a faculty member is an associate professor?
|| BS || Education || Social Sciences || Total ||
=========================================================
Male || 10 || 26 || 19 || 55 ||
=========================================================
Female || 15 || 21 || 17 || 53 ||
=========================================================
Total || 25 || 47 || 36 || 108 ||
=========================================================
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

	Biological Science	Education	Social Sciences	Total
Male	10	26	19	55
Female	15	21	17	53
Total	25	47	36	108

15 female faculty members in Biological Science.
21 female faculty members in Education.
15+21 = 36 total female faculty members from either field.
1/6 of 36 = 6 female associate professors in Biological Science and Education combined.

10 male faculty members in Biological Science.
26 male faculty members in Education.
10+26 = 36 total male faculty members from either field.
1/4 of 36 = 9 male associate professors in Biological Science and Education combined.

6 female + 9 male = 15 total associate professors from the two fields mentioned.
Let A = 15 so we can use it later.

There are 25 faculty members from Biological Science and 47 from Education.
That gives 25+47 = 72 total faculty members.
Let B = 72.
We ignore the social sciences entirely because of the phrasing "a person is randomly chosen from these two departments", and those two departments are of course Biological Science and Education.

We have A = 15 faculty members who are associate professors in either of the two fields mentioned.
This is out of B = 72 faculty members total from these two fields.

Divide A over B
A/B = 15/72 = (3*5)/(3*24) = 5/24

Answer: 5/24

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